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It is a 2nd-order system, because it swings in a repetitive motion at a certain frequency like, say, 30 swings per minute.
It also is damped, because if you set it swinging and then leave it alone, it rubs against the air and its swings becomes smaller and smaller until it seems to have stopped.

Now, if you give a shove (put energy into it) at the same frequency that it swings (30 times per minute), the swings will get larger and larger until they get really large.
That's what happens when you drive a 2nd-order system at its resonant frequency.

@daaxix There are pervasive myths about the Tacoma Narrows collapse. It was not a straightforward case of resonance forcing as is usually presented - engineers already knew about resonances at the time! Rather it was a strongly non-linear phenomenon, something harder to predict (ketchum.org/billah/Billah-Scanlan.pdf). A simple driven pendulum, spring, or LC circuit is a better analogy.
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Michael BrownJan 19 '13 at 10:10

Ok, the aeroelastic flutter excited a torsional mode, still at resonance (in a damping coefficient). I read the paper, and they model the bridge mode and excitation using a different differential equation than is usually used in a pendulum or mass spring resonance model, but it is still exciting a mode at resonance, and I argue a semantic difference...
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daaxixJan 19 '13 at 15:25